Screening machines, that is, machines having one or more screens for sizing, sifting, or separating particulate materials by vibratory, oscillatory, or gyratory movement of the screen, are in widespread commercial use. The screen or screens of such machines are mounted and housed within an enclosure called a screen box. The box provides a housing which prevents dust or fines from escaping during operation, as well as preventing outside dirt from contaminating the product being screened. One example of such machines is the "Rotex" brand machine produced and sold by the assignee of this application. The particle mix to be separated is introduced into the box and deposited on the screen; screening movement applied to the box separates different size or shape fractions of the particulate feed according to the size and shape of the screen openings. The material to be screened is fed from a source such as a hopper or elevator to an inlet conduit and falls through an opening in a so-called "top cover" over the screen box, onto the top screen. After separation by the screen, the various separated fractions fall from the screen box to one or more separate outlet conduits. Because the box moves in a rapid screening motion, provision must be made for accommodating its motion relative to stationary inlet and outlet conduits while still enclosing the falling particles and preventing dust from escaping from the screen box.